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On the almost automorphy of bounded solutions of differential equations with piecewise constant argument. (English) Zbl 1115.34068

The authors give sufficient spectral conditions for the almost automorphy of bounded solutions to differential equations with piecewise constant argument of the form \[ x'(t)=Ax([t])+f(t), \] where \(A\) is a bounded linear operator in \(X\) and \(f\) is an \(X\)-valued almost automorphic function.

MSC:

34K14 Almost and pseudo-almost periodic solutions to functional-differential equations
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